Based on previous knowledge, it seems that when the number of spiked eigenvalues is small, the influence caused by spiked part is little and the distribution of LSS is mainly decided by the bulk part, however, that is not the case. After sumlations, a surprise is that when the spiked eigenvalues is very large, LSS will also affected by the spiked part even though the number of spike is small. Some useful results we refer to [1]}, which is comprehensive and indepth.
